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Ukrainian Mathematical Journal

, Volume 43, Issue 9, pp 1170–1173 | Cite as

A problem of Fekete

  • O. M. Katkova
Brief Communications
  • 27 Downloads

Abstract

The problem of whether an entire function f with nonnegative coefficients can be multiplied by another entire function g which “grows not faster” than f so that the product fg is a generating function of a Pólya frequency sequence of finite order (multipositive sequence in the sense of Fekete) is investigated.

Keywords

Entire Function Finite Order Frequency Sequence Nonnegative Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature cited

  1. 1.
    S. Karlin, Total Positivity, Vol. 1, Stanford University Press, Stanford (1968).Google Scholar
  2. 2.
    M. Fekete and G. Pólya, “Über ein Problem von Laguerre,” Rend. Circ. Mat. Palermo,34, 89–120 (1912).Google Scholar
  3. 3.
    O. M. Katkova and I. V. Ostrovskii, “Null sets of entire generating functions of the Pólya frequency sequences of finite order,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 13–15 (1988).Google Scholar
  4. 4.
    O. M. Katkova and I. V. Ostrovskii, “On null sets of entire generating functions of the Pólya frequency sequences of finite order,” Izv. Akad. Nauk SSSR, Ser. Mat.,53, No. 4, 771–781 (1989).Google Scholar
  5. 5.
    O. M. Katkova, “On indicators of entire functions of finite order with multipositive sequences of coefficients,” deposited at VINITI, Kharkov, No. 6 (1989).Google Scholar
  6. 6.
    O. M. Katkova, “On a method of construction of the Pólya frequency sequences,” Teor. Funkts. Anal. Ikh Prilozh., No. 51, 129–137 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • O. M. Katkova
    • 1
  1. 1.Kharkov UniversityUSSR

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